The perimeter of the triangle is 25 meters. The first side is 7 meters longer than the third side. The second side is 4 times the length of the third side. Find the sides of the triangles
if the 3rd side is x, then
x+7 + 4x + x = 25
x = 3
Now you know the 3 lengths
let the third side be x m
the the first side be x+7 m
the second side is 4x m
x + x+7 + 4x = 25
6x = 18
x = 3
the sides are 3 m, 10 m, and 12 m
f = first side
s = second side
t = third side
The first side is 7 meters longer than the third side. means:
f = t + 7
The second side is 4 times the length of the third side neans:
s = 4 t
Perimeter:
P = f + s + t = 25
t + 7 + 4 t + t = 25
6 t + 7 = 25
6 t = 25 - 7 = 18
t = 18 / 6 = 3
f = t + 7 = 3 + 7 = 10
s = 4 t = 4 • 3 = 12
First side = 10 m
Second side = 12 m
Third side = 3 m
To solve this problem, we can set up equations based on the given information and then solve them simultaneously. Let's denote the length of the third side as "x".
Given:
Perimeter of the triangle = 25 meters
First side = 7 meters longer than the third side (x)
Second side = 4 times the length of the third side (4x)
The perimeter of a triangle is the sum of all its sides. So, we can write the equation as:
x + (x + 7) + 4x = 25
Let's solve this equation step by step:
Combine like terms on the left side:
6x + 7 = 25
Subtract 7 from both sides to isolate the term with x:
6x = 18
Divide both sides by 6 to solve for x:
x = 3
Now that we have found the value of x (the length of the third side), we can substitute it back into the given equations to find the lengths of the other sides.
First side: x + 7 = 3 + 7 = 10 meters
Second side: 4x = 4 * 3 = 12 meters
So, the sides of the triangle are:
First side: 10 meters
Second side: 12 meters
Third side: 3 meters